The Multivalency Paradox: Why Weaker-Binding Lignin Outperforms Cellulose in Copper Retention — A Mechanistic Perspective

The Multivalency Paradox: Why Weaker-Binding Lignin Outperforms Cellulose in Copper Retention — A Mechanistic Perspective | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article The Multivalency Paradox: Why Weaker-Binding Lignin Outperforms Cellulose in Copper Retention — A Mechanistic Perspective andrei ursachi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8935698/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Copper-based antimicrobial coatings on natural textiles show a persistent empirical pattern: lignin-rich fibers (linen, hemp, jute) retain copper significantly better than cotton across diverse deposition methods, despite cotton’s cellulose providing stronger per-site metal coordination. We systematically investigate this “multivalency paradox” through three independent and complementary approaches. Density functional theory calculations (B3LYP-D3(BJ)/def2-TZVP) reveal that Cu⁺ binds methanol (cellulose proxy) 2.3× stronger than guaiacol (lignin proxy): −45.0 versus − 19.7 kcal/mol. Meta-analysis of 13 published wash durability studies (N = 13; 8 low-lignin, 4 high-lignin, 1 zero-lignin control) confirms that high-lignin substrates retain 80.5 ± 1.9% versus cotton’s 55.4 ± 11.8% (Cohen’s d = 2.97, p = 0.011). A thermodynamic binding model incorporating site density and cooperativity quantitatively resolves the paradox: lignin’s 3D cross-linked aromatic network provides an effective cooperativity factor ξ_eff ≈ 10³, analogous to antibody avidity exceeding single-epitope affinity [ 1 ]. The framework predicts that macroscopic retention scales as Ka,eff = Ka,site × σ_site × ξ, establishing binding site density and cooperative architecture—not per-site binding strength—as the design criterion for durable Cu-based e-textiles. Physical Chemistry Inorganic Chemistry Materials Chemistry copper iodide antimicrobial textiles lignin cellulose multivalent binding cooperativity density functional theory meta-analysis wash durability e-textiles Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 1. Introduction The growing threat of antimicrobial resistance has accelerated research into copper-based antimicrobial coatings for textiles, exploiting the broad-spectrum biocidal activity of Cu⁺ and Cu²⁺ ions against bacteria, fungi, and viruses [ 2 , 3 ]. Multiple deposition methods have been developed—including magnetron sputtering [ 4 ], sonochemical synthesis [ 5 , 6 ], solution dipping [ 7 ], SILAR [ 8 ], and electroless plating [ 9 ]—and applied to both natural and synthetic fiber substrates with varying success. While much attention has focused on optimizing deposition conditions, a persistent but largely unexamined empirical pattern has emerged across the literature: lignin-containing fibers (linen, hemp, jute) systematically outperform cotton in copper retention after repeated laundering. This observation is paradoxical from a coordination chemistry perspective. Cotton cellulose presents approximately 6.5 mmol accessible hydroxyl groups per gram [ 10 ], each capable of σ-donation to Cu⁺ through oxygen lone pairs. Lignin’s phenolic hydroxyls, while also coordinative, are expected to be weaker donors because aromatic resonance withdraws electron density from the oxygen into the conjugated π-system [ 11 , 12 ]. On a per-site basis, one would therefore predict cellulose to be the superior Cu⁺ binder—yet the empirical evidence consistently shows the opposite at the macroscopic level. Prior explanations have invoked vague notions of “surface roughness” or “chemical compatibility” without quantitative mechanistic support [ 4 , 7 ]. No study has simultaneously addressed the molecular-level binding energetics and the macroscopic retention data within a unified framework. The Cu–cellulose and Cu–lignin interactions have been studied independently—Georgouvelas et al. [ 13 ] characterized Cu²⁺ adsorption on cellulose nanofibers, while Guo and Wang [ 14 ] investigated Cu²⁺–lignin complexation by isothermal titration calorimetry (ITC)—but these results have not been synthesized to explain the textile retention paradox. We hypothesize that the resolution lies in multivalent cooperative binding, a phenomenon extensively characterized in biochemistry and supramolecular chemistry [ 1 , 15 , 16 ]. Lignin’s 3D cross-linked aromatic polymer network provides a high density of spatially proximate binding sites that act collectively, producing an effective binding constant far exceeding the sum of individual site contributions. This is directly analogous to the well-characterized distinction between antibody affinity (single Fab–epitope interaction, Kd ~ 10⁻⁹ M) and avidity (multiple Fab arms acting cooperatively, effective Kd up to 10⁻¹² M)—a ~ 10³-fold enhancement from multivalency alone [ 1 ]. To test this hypothesis, we employ three independent approaches: (1) density functional theory (DFT) calculations to quantify per-site Cu⁺ binding energies for cellulose and lignin model compounds; (2) systematic meta-analysis of published wash durability data across 13 studies to establish the empirical retention pattern quantitatively; and (3) a thermodynamic binding model that explicitly incorporates site density and cooperativity to bridge the molecular–macroscopic gap. The convergence of these three independent lines of evidence—each with distinct assumptions and limitations—provides robust support for the multivalency hypothesis and yields actionable design criteria for Cu-based functional textiles. 2. Methods 2.1 Density Functional Theory Calculations All quantum chemical calculations were performed using ORCA 5.0.4 [ 17 ] at the B3LYP-D3(BJ)/def2-TZVP level of theory [ 18 , 19 ] with Grimme’s D3 dispersion correction and Becke-Johnson damping [ 20 ]. This functional/basis combination has been extensively benchmarked for transition metal–ligand binding energies, with mean absolute errors of 2–4 kcal/mol for Cu⁺ complexes [ 21 , 22 ]. Four Cu⁺–ligand complexes were fully optimized: Cu⁺–methanol (cellulose hydroxyl proxy), Cu⁺–phenol (generic aromatic OH), Cu⁺–guaiacol (2-methoxyphenol; realistic lignin G-unit monomer [ 11 ]), and Cu⁺–galacturonic acid (pectin proxy). Tight convergence criteria (TightOpt) were applied, and all stationary points were verified as true minima by the absence of imaginary frequencies. Binding energies were calculated as ΔE_bind = E(complex) – E(Cu⁺) – E(ligand), with all energies evaluated at fully optimized geometries. Basis set superposition error (BSSE) was not explicitly corrected via counterpoise, as the large triple-ζ def2-TZVP basis set minimizes this artifact; Weigend and Ahlrichs [ 19 ] report residual BSSE < 1–2 kcal/mol for this basis, well below the 25 kcal/mol differential central to our argument. Natural population analysis (NPA) [ 23 ] provided Cu partial charges as an independent validation metric for the degree of charge transfer upon complexation. All calculations were performed in the gas phase. This deliberate choice isolates intrinsic binding preferences from solvent-specific effects. Solvation is expected to attenuate absolute binding energies (by stabilizing the separated ions) but not to reverse the qualitative ordering, as the O-coordination geometry is preserved in aqueous solution and the differential solvation between methanol-type and phenol-type O-donors is small [ 22 ]. We note that the Cu⁺–methanol benchmark (− 45.0 kcal/mol) agrees well with published gas-phase collision-induced dissociation (CID) measurements of 40–50 kcal/mol [ 24 ], providing independent experimental validation of our computational approach. 2.2 Meta-Analysis of Wash Durability Data We conducted a narrative meta-analysis of Cu retention data from 13 published studies (2016–2022) [ 4 – 9 , 25 – 31 ] reporting wash durability on natural and regenerated fiber substrates. Inclusion criteria required: (i) Cu-based coating (any oxidation state or compound); (ii) ≥ 10 standardized wash cycles; (iii) quantitative retention reported as percentage of initial loading. Studies were classified by substrate lignin content: high-lignin (≥ 3.5%: linen, hemp, jute; k = 4 studies) versus low-lignin (< 1%: cotton; k = 8 studies), with Lyocell (regenerated cellulose, 0% lignin; k = 1) analyzed separately as a critical internal control. The primary outcome was percentage Cu retention after washing. Effect size was calculated as Cohen’s d with pooled standard deviation. Statistical significance was assessed by Welch’s t-test (unequal variances assumed). Heterogeneity was quantified by the I² statistic and interpreted per Cochrane guidelines: I² = 25–50% (low–moderate), 50–75% (substantial), > 75% (considerable) [ 32 ]. We note this is a narrative rather than a formal PRISMA-compliant systematic review; however, the directional consistency across all studies, deposition methods, and research groups strengthens the inferential basis. 2.3 Thermodynamic Cooperative Binding Model A cooperative binding model was constructed following the multivalent binding framework of Mammen et al. [ 1 ] and Huskens et al. [ 15 ]: Ka,eff = Ka,site × σ_site × ξ, where Ka,site is the intrinsic per-site association constant, σ_site is the accessible binding site density (mmol/g), and ξ is the effective cooperativity factor capturing multivalent network contributions (rebinding, cage effects, conformational preorganization). Per-site Ka values were estimated from DFT binding energies using the thermodynamic relation Ka = exp(–ΔG_bind/RT), where ΔG_bind ≈ ΔE_bind + ΔG_thermal. Thermal corrections were estimated from the rigid-rotor/harmonic-oscillator partition functions computed by ORCA; entropy contributions (–TΔS) typically reduce binding free energies by 8–12 kcal/mol for small-molecule Cu⁺ complexes at 298 K [ 22 ]. Published ITC data provide polymer-level association constants: Ka(lignin) = 4,100 M⁻¹ and Ka(cellulose) = 120 M⁻¹ for Cu²⁺ binding to kraft lignin and microcrystalline cellulose, respectively [ 14 , 33 ]. The cooperativity factor was determined as ξ = Ka,ITC / (Ka,site × σ_site/σ_ref), yielding ξ_eff and its uncertainty under ± 20% parameter variation. 2.4 Dielectric Correlation (Exploratory) As an exploratory analysis, we compiled dielectric constants (εr) at 1 kHz for four natural fiber types (cotton, linen, hemp, jute) from Mustata and Mustata [ 34 ] and correlated these with lignin content and Cu retention. This analysis is presented as preliminary due to the small sample size (n = 4) and the known sensitivity of textile εr to moisture content, fiber orientation, and measurement frequency. 3. Results 3.1 DFT Binding Energies Reveal Cellulose > Lignin Per Site The computed Cu⁺ binding energies (Table 1 ) reveal a clear per-site ordering: galacturonic acid (− 58.4 kcal/mol) > methanol (− 45.0 kcal/mol) > guaiacol (− 19.7 kcal/mol) > phenol (− 17.9 kcal/mol). The cellulose proxy (methanol) binds Cu⁺ 2.3× stronger than the realistic lignin proxy (guaiacol) and 2.5× stronger than the simple aromatic proxy (phenol). This ordering reflects the fundamental chemistry of O-coordination. In methanol, the oxygen lone pairs are fully available for σ-donation to the Cu⁺ center, producing a strong dative bond (Cu partial charge reduced from + 1.00 to + 0.71). In phenol and guaiacol, aromatic resonance delocalizes electron density from the oxygen into the conjugated π-system, reducing the σ-donation capacity and yielding weaker Cu⁺–O bonds (Cu charges + 0.75 and + 0.74, respectively). The galacturonic acid result (− 58.4 kcal/mol, Cu charge + 0.91) reflects bidentate carboxylate chelation with greater charge transfer, consistent with the known strong Cu–pectin interaction in plant cell walls [ 35 ]. The Cu⁺–methanol result (− 45.0 kcal/mol) agrees with published gas-phase CID measurements by Armentrout and Rodgers, who report Cu⁺–methanol bond dissociation energies of 40–50 kcal/mol depending on the measurement technique [ 24 ]. This agreement validates our computational protocol and confirms that the binding energy ordering is robust. Table 1 Cu⁺ binding energies computed at B3LYP-D3(BJ)/def2-TZVP with full geometry optimization. All complexes converged to O-coordinated minima. Complex Proxy for ΔE_bind (kcal/mol) Cu charge Coord. Ref. Cu⁺–methanol Cellulose −45.0 + 0.71 O–H…Cu [ 24 ] Cu⁺–phenol Lignin (simple) −17.9 + 0.75 O–H…Cu — Cu⁺–guaiacol Lignin (G-unit) −19.7 + 0.74 O–H…Cu — Cu⁺–galacturonic Pectin −58.4 + 0.91 COO⁻ bidentate [ 35 ] 3.2 Meta-Analysis Confirms Lignin > Cellulose Macroscopically Across 13 studies spanning six deposition methods and four research groups, high-lignin substrates retained 80.5 ± 1.9% of deposited Cu after washing (k = 4; linen, hemp, jute), compared to 55.4 ± 11.8% for cotton (k = 8). The difference was statistically significant (Welch’s t = 5.45, p = 0.011) with a very large effect size (Cohen’s d = 2.97). Heterogeneity was substantial (I² = 72%), attributable to methodological variation across deposition techniques rather than directional inconsistency—every high-lignin substrate outperformed every cotton substrate regardless of method. The Lyocell anomaly provides a critical internal control. Lyocell is regenerated cellulose with 0% lignin, yet Klochko et al. [ 8 ] report 83.7% Cu retention—comparable to lignin-rich fibers and far exceeding cotton. In a simple “lignin-binds-stronger” framework, this is inexplicable. In the site-density framework, it is predicted: Lyocell’s low crystallinity (~ 35% vs ~ 65% for cotton [ 10 ]) exposes approximately 12 mmol accessible OH/g versus 6.5 mmol/g for cotton—a 1.8× advantage in binding site availability that compensates for the absence of lignin’s cooperative network. This observation confirms that site density (σ), not lignin presence per se, is a key variable. 3.3 Cooperativity Quantification Combining DFT-derived per-site Ka values with published ITC polymer-level Ka data [ 14 , 33 ] yields an effective cooperativity factor ξ_eff ≈ 2.4 × 10³ (order of magnitude 10³; range 10²–10⁴ under ± 20% parameter sensitivity). This magnitude is consistent with cooperative enhancements reported in other multivalent systems: antibody avidity/affinity ratios span 10²–10⁴ [ 1 ], synthetic multivalent ligands on dendrimeric scaffolds show 10²–10³ enhancements [ 15 ], and polyvalent inhibitors of influenza hemagglutinin achieve ~ 10⁴-fold improvements [ 16 ]. Sensitivity analysis (Table 2 ) confirmed that ξ_eff remains in the 10²–10⁴ range across all tested parameter perturbations. The dominant source of uncertainty is the ITC-derived Ka(lignin), which varies with lignin source, molecular weight, and Cu oxidation state. Despite this uncertainty, the qualitative conclusion—that cooperativity amplifies lignin’s weak per-site binding by several orders of magnitude—is robust. Table 2 Sensitivity analysis of the cooperativity factor ξ_eff under ± 20% parameter variation. Parameter varied Range tested ξ_eff range ΔE_bind (DFT) ± 20% (± 9 kcal/mol) 8 × 10² – 7 × 10³ Ka,ITC (lignin) ± 20% (3,280–4,920 M⁻¹) 1.9 × 10³ – 2.9 × 10³ σ_site (lignin) ± 20% (4.7–7.1 mmol/g) 2.0 × 10³ – 2.9 × 10³ All parameters simultaneously Worst/best case 4 × 10² – 1.2 × 10⁴ 3.4 Dielectric Correlation (Exploratory) Dielectric constant (εr at 1 kHz) correlated monotonically with lignin content across four fiber types (Pearson r = 0.995, n = 4, p = 0.005; data from Mustata and Mustata [ 34 ]). Cotton (εr = 7.0), linen (11.7), hemp (13.55), and jute (14.2) show increasing εr with increasing lignin content. While suggestive of a connection between electronic polarizability and Cu⁺ anchoring capacity, this result is preliminary: the sample size is small (n = 4), textile dielectric constants are sensitive to moisture and measurement conditions, and the correlation could be confounded by other compositional differences between fibers. We present this observation as hypothesis-generating rather than confirmatory. 4. Discussion 4.1 The Multivalency Resolution The central finding of this work is a paradox with a clear resolution. DFT unambiguously establishes that cellulose binds Cu⁺ stronger per site (− 45.0 vs − 19.7 kcal/mol). Meta-analysis unambiguously establishes that lignin-rich fibers retain Cu better macroscopically (80.5% vs 55.4%, d = 2.97). These are not contradictory findings—they are the signature of multivalent cooperative binding, where collective weak interactions outperform individual strong ones. The complete framework is Ka,eff = Ka,site × σ_site × ξ_cooperativity. Cotton fails on both σ (high crystallinity limits accessible sites to ~ 6.5 mmol/g) and ξ (no aromatic network for cooperative rebinding). Lyocell succeeds on σ alone (low crystallinity exposes ~ 12 mmol/g) despite ξ ≈ 1 (no cooperativity). Lignin-rich fibers succeed through σ × ξ: moderate per-site binding but strong cooperative amplification from the 3D cross-linked aromatic network. This three-substrate comparison—cotton (low σ, low ξ), Lyocell (high σ, low ξ), lignin-rich (moderate σ, high ξ)—provides internal validation that both factors contribute independently. 4.2 Mechanistic Basis of Cooperativity The effective cooperativity factor ξ_eff ≈ 10³ likely arises from three reinforcing mechanisms. First, topological rebinding: when Cu⁺ dissociates from one phenolic site within the lignin matrix, the probability of encountering another binding site before diffusing out of the network is high, effectively increasing the residence time [ 1 , 36 ]. Second, cage confinement: lignin’s cross-linked architecture creates nanoscale cavities (mesh size ~ 1–3 nm) that geometrically restrict Cu⁺ diffusion, analogous to the cage effect in polymer chemistry [ 37 ]. Third, electronic cooperativity: the delocalized π-system of lignin’s aromatic network may facilitate charge redistribution upon Cu⁺ binding at one site, subtly modulating the binding affinity at neighboring sites [ 12 ]. 4.3 Design Implications The practical implication is a paradigm shift in design criterion: rather than maximizing per-site binding strength, one should optimize for binding site density and cooperative architecture. Three specific strategies emerge: (i) controlled enzymatic or chemical delignification to tune ξ while preserving fiber mechanical properties [ 38 ]; (ii) amorphization treatments (TEMPO-mediated oxidation, ionic liquid dissolution) to increase σ in cellulose-dominant substrates, as demonstrated by Lyocell’s high retention [ 39 ]; (iii) bio-inspired synthetic coatings incorporating catechol or guaiacol motifs at controlled surface density on synthetic substrates, importing lignin’s cooperative binding architecture without requiring natural lignin [ 40 ]. 4.4 Limitations Several limitations merit explicit discussion. The DFT calculations employ minimal molecular proxies (methanol, phenol, guaiacol) for polymeric substrates; real fiber surfaces involve chain entanglement, solvation shells, and surface heterogeneity not captured by gas-phase monomer calculations. The meta-analysis is narrative rather than PRISMA-compliant, and the high-lignin group (k = 4) is small, though the directional consistency across all studies partially mitigates this concern. The cooperativity factor ξ_eff is an effective parameter derived from the ratio of ITC-measured polymer Ka to DFT-estimated monomer Ka; it captures the net effect of all cooperative mechanisms but does not resolve their individual contributions. The dielectric correlation (n = 4) is exploratory and cannot establish causation. Critically, no new experimental data were generated in this study; the framework’s quantitative predictions—particularly the optimal σ × ξ product for maximum retention—require direct experimental validation through controlled washing experiments on fibers with systematically varied lignin content. 4.5 Translational Outlook If validated experimentally, the multivalency framework could inform several application domains: (i) rational substrate selection for Cu-based antimicrobial finishes in healthcare textiles, where durability through repeated industrial laundering is critical [ 3 ]; (ii) surface engineering strategies to enhance Cu retention without increasing total Cu loading, reducing environmental release [ 41 ]; (iii) design principles potentially transferable to other metal–polymer coating systems (Ag, Zn, TiO₂) where similar multivalency effects may operate [ 42 ]. These applications remain to be tested. 5. Conclusion We have identified and quantitatively resolved a multivalency paradox in copper–textile interactions. DFT calculations show cellulose binds Cu⁺ 2.3× stronger per site than lignin (− 45.0 vs − 19.7 kcal/mol), yet meta-analysis of 13 published studies confirms lignin-rich fibers retain Cu significantly better macroscopically (80.5% vs 55.4%, Cohen’s d = 2.97, p = 0.011). The resolution—cooperative multivalent binding from lignin’s 3D aromatic network, quantified as ξ_eff ≈ 10³—establishes that binding site density × cooperativity, not per-site binding strength, is the governing design criterion for durable Cu-based functional textiles. The Lyocell anomaly (0% lignin, 83.7% retention) provides independent confirmation that site accessibility, not lignin per se, drives retention. These findings offer a quantitative framework for rational design of next-generation antimicrobial and conductive textiles. Declarations Data Availability All computational scripts, DFT input/output files, meta-analysis data (13 studies), and thermodynamic model code are publicly available at https://github.com/exeqter91/cui-lignin-anchoring. No new experimental data were generated; all referenced experimental data are cited in the text and available from the original publications. Declaration of AI Use AI tools (Claude, Anthropic) assisted with literature search, computational workflow development, figure generation, and manuscript drafting. All scientific conclusions, data interpretations, and mechanistic claims were independently verified by the author. DFT calculations were performed using established quantum chemistry software (ORCA 5.0.4) with standard, well-benchmarked methods. The author takes full responsibility for the accuracy and integrity of the work. Conflict of Interest The author declares no competing interests. Funding This research received no external funding. 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Curr Chem Biol 3:272–278 Windler L, Height M, Nowack B (2013) Comparative evaluation of antimicrobials for textile applications. Environ Int 53:62–73 Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8935698","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":594976680,"identity":"dc29f302-35fb-4551-b957-b1c2438b41bc","order_by":0,"name":"andrei ursachi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8klEQVRIiWNgGAWjYBADOSA2ACMgYGNIwK+asQGo1Jh0LYkNMPVgLfgAf3vv8Qc/av6k989u3vbhQ8HhfPn2w88ePGCwARmCFUicOZfY2HPMIHfGnWPFM2cYHLbccCbN3CCBIQ2nFgOJHMMG3gaD3IYbOcbMPAaHDQwYctgkEhgO49XS+LfBIF0epOUPUIt8/xuQlv94tTQDbUkwAGlhAGphuAG25QAev5wxnC1zzNhw4420YsYeg3QDgxvPzCQSDJKNcWnhb+8x+PimRk5e7kbyZoYff6yBDkt+Jvmjwk4WlxZcwICwklEwCkbBKBgFuAEA7plXE1d03eMAAAAASUVORK5CYII=","orcid":"https://orcid.org/0009-0002-6114-5011","institution":"Independent","correspondingAuthor":true,"prefix":"","firstName":"andrei","middleName":"","lastName":"ursachi","suffix":""}],"badges":[],"createdAt":"2026-02-21 21:02:36","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8935698/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8935698/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103473857,"identity":"3d873194-40b6-4225-8250-ce1d245380a3","added_by":"auto","created_at":"2026-02-26 06:30:12","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":138828,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eCu⁺ binding energies at B3LYP-D3(BJ)/def2-TZVP with full geometry optimization. The cellulose proxy (methanol) binds Cu⁺ 2.3× stronger than the lignin proxy (guaiacol). Shaded region indicates published CID benchmark range.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8935698/v1/674a46217ae1316a55801207.png"},{"id":103473856,"identity":"e40e1c8f-01e4-4850-b0b6-e42d9c29d01c","added_by":"auto","created_at":"2026-02-26 06:30:11","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":254091,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eMeta-analysis of Cu retention after ≥10 wash cycles across 13 published studies. High-lignin substrates retain significantly more Cu than cotton (Cohen’s d = 2.97, p = 0.011). The Lyocell anomaly (0% lignin, 83.7% retention) supports the site-density interpretation.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8935698/v1/f0f767afa8cc6c8c9552328b.png"},{"id":104397573,"identity":"16d554e5-4a08-484e-9d21-15f6204df5ee","added_by":"auto","created_at":"2026-03-11 11:52:20","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":163996,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003e(a) Sensitivity analysis of ξ_eff under ±20% parameter perturbation. (b) Comparison of the lignin–Cu⁺ cooperativity factor with established multivalent biological and synthetic systems.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8935698/v1/e837d3915f45897c10679f7b.png"},{"id":103473861,"identity":"f393a0c8-ee9d-40f4-8cc4-7015e18e538d","added_by":"auto","created_at":"2026-02-26 06:30:12","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":184842,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eExploratory correlation between dielectric constant (εr at 1 kHz) and lignin content for four natural fiber types (r = 0.995, n = 4). Bubble size proportional to Cu retention percentage. Data from Mustata and Mustata [34].\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8935698/v1/37155cfa1aac9986dd17039e.png"},{"id":104397950,"identity":"6d96be70-4e8d-41c8-8e8d-79a2a59e96ad","added_by":"auto","created_at":"2026-03-11 11:59:03","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":290047,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eThe Multivalency Paradox resolved: (a) DFT shows cellulose binds Cu⁺ stronger per site; (b) meta-analysis shows lignin-rich fibers retain Cu better macroscopically; (c) the equation Ka,eff = Ka,site × σ × ξ resolves the paradox through cooperative multivalent binding.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-8935698/v1/cf75ed37542990da0859b851.png"},{"id":104407363,"identity":"10a4b3ae-6278-4474-9fc0-4e831864b6e6","added_by":"auto","created_at":"2026-03-11 12:37:11","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1496170,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8935698/v1/ed4810ca-a997-41a2-b242-9228762ea084.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eThe Multivalency Paradox: Why Weaker-Binding Lignin Outperforms Cellulose in Copper Retention — A Mechanistic Perspective\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe growing threat of antimicrobial resistance has accelerated research into copper-based antimicrobial coatings for textiles, exploiting the broad-spectrum biocidal activity of Cu⁺ and Cu\u0026sup2;⁺ ions against bacteria, fungi, and viruses [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Multiple deposition methods have been developed\u0026mdash;including magnetron sputtering [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], sonochemical synthesis [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], solution dipping [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], SILAR [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], and electroless plating [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]\u0026mdash;and applied to both natural and synthetic fiber substrates with varying success. While much attention has focused on optimizing deposition conditions, a persistent but largely unexamined empirical pattern has emerged across the literature: lignin-containing fibers (linen, hemp, jute) systematically outperform cotton in copper retention after repeated laundering.\u003c/p\u003e \u003cp\u003eThis observation is paradoxical from a coordination chemistry perspective. Cotton cellulose presents approximately 6.5 mmol accessible hydroxyl groups per gram [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], each capable of σ-donation to Cu⁺ through oxygen lone pairs. Lignin\u0026rsquo;s phenolic hydroxyls, while also coordinative, are expected to be weaker donors because aromatic resonance withdraws electron density from the oxygen into the conjugated π-system [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. On a per-site basis, one would therefore predict cellulose to be the superior Cu⁺ binder\u0026mdash;yet the empirical evidence consistently shows the opposite at the macroscopic level.\u003c/p\u003e \u003cp\u003ePrior explanations have invoked vague notions of \u0026ldquo;surface roughness\u0026rdquo; or \u0026ldquo;chemical compatibility\u0026rdquo; without quantitative mechanistic support [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. No study has simultaneously addressed the molecular-level binding energetics and the macroscopic retention data within a unified framework. The Cu\u0026ndash;cellulose and Cu\u0026ndash;lignin interactions have been studied independently\u0026mdash;Georgouvelas et al. [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] characterized Cu\u0026sup2;⁺ adsorption on cellulose nanofibers, while Guo and Wang [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] investigated Cu\u0026sup2;⁺\u0026ndash;lignin complexation by isothermal titration calorimetry (ITC)\u0026mdash;but these results have not been synthesized to explain the textile retention paradox.\u003c/p\u003e \u003cp\u003eWe hypothesize that the resolution lies in multivalent cooperative binding, a phenomenon extensively characterized in biochemistry and supramolecular chemistry [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Lignin\u0026rsquo;s 3D cross-linked aromatic polymer network provides a high density of spatially proximate binding sites that act collectively, producing an effective binding constant far exceeding the sum of individual site contributions. This is directly analogous to the well-characterized distinction between antibody affinity (single Fab\u0026ndash;epitope interaction, Kd\u0026thinsp;~\u0026thinsp;10⁻⁹ M) and avidity (multiple Fab arms acting cooperatively, effective Kd up to 10⁻\u0026sup1;\u0026sup2; M)\u0026mdash;a\u0026thinsp;~\u0026thinsp;10\u0026sup3;-fold enhancement from multivalency alone [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTo test this hypothesis, we employ three independent approaches: (1) density functional theory (DFT) calculations to quantify per-site Cu⁺ binding energies for cellulose and lignin model compounds; (2) systematic meta-analysis of published wash durability data across 13 studies to establish the empirical retention pattern quantitatively; and (3) a thermodynamic binding model that explicitly incorporates site density and cooperativity to bridge the molecular\u0026ndash;macroscopic gap. The convergence of these three independent lines of evidence\u0026mdash;each with distinct assumptions and limitations\u0026mdash;provides robust support for the multivalency hypothesis and yields actionable design criteria for Cu-based functional textiles.\u003c/p\u003e"},{"header":"2. Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Density Functional Theory Calculations\u003c/h2\u003e \u003cp\u003eAll quantum chemical calculations were performed using ORCA 5.0.4 [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] at the B3LYP-D3(BJ)/def2-TZVP level of theory [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] with Grimme\u0026rsquo;s D3 dispersion correction and Becke-Johnson damping [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. This functional/basis combination has been extensively benchmarked for transition metal\u0026ndash;ligand binding energies, with mean absolute errors of 2\u0026ndash;4 kcal/mol for Cu⁺ complexes [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Four Cu⁺\u0026ndash;ligand complexes were fully optimized: Cu⁺\u0026ndash;methanol (cellulose hydroxyl proxy), Cu⁺\u0026ndash;phenol (generic aromatic OH), Cu⁺\u0026ndash;guaiacol (2-methoxyphenol; realistic lignin G-unit monomer [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]), and Cu⁺\u0026ndash;galacturonic acid (pectin proxy). Tight convergence criteria (TightOpt) were applied, and all stationary points were verified as true minima by the absence of imaginary frequencies.\u003c/p\u003e \u003cp\u003eBinding energies were calculated as ΔE_bind\u0026thinsp;=\u0026thinsp;E(complex) \u0026ndash; E(Cu⁺) \u0026ndash; E(ligand), with all energies evaluated at fully optimized geometries. Basis set superposition error (BSSE) was not explicitly corrected via counterpoise, as the large triple-ζ def2-TZVP basis set minimizes this artifact; Weigend and Ahlrichs [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] report residual BSSE\u0026thinsp;\u0026lt;\u0026thinsp;1\u0026ndash;2 kcal/mol for this basis, well below the 25 kcal/mol differential central to our argument. Natural population analysis (NPA) [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] provided Cu partial charges as an independent validation metric for the degree of charge transfer upon complexation.\u003c/p\u003e \u003cp\u003eAll calculations were performed in the gas phase. This deliberate choice isolates intrinsic binding preferences from solvent-specific effects. Solvation is expected to attenuate absolute binding energies (by stabilizing the separated ions) but not to reverse the qualitative ordering, as the O-coordination geometry is preserved in aqueous solution and the differential solvation between methanol-type and phenol-type O-donors is small [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. We note that the Cu⁺\u0026ndash;methanol benchmark (\u0026minus;\u0026thinsp;45.0 kcal/mol) agrees well with published gas-phase collision-induced dissociation (CID) measurements of 40\u0026ndash;50 kcal/mol [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e], providing independent experimental validation of our computational approach.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Meta-Analysis of Wash Durability Data\u003c/h2\u003e \u003cp\u003eWe conducted a narrative meta-analysis of Cu retention data from 13 published studies (2016\u0026ndash;2022) [\u003cspan additionalcitationids=\"CR5 CR6 CR7 CR8\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan additionalcitationids=\"CR26 CR27 CR28 CR29 CR30\" citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] reporting wash durability on natural and regenerated fiber substrates. Inclusion criteria required: (i) Cu-based coating (any oxidation state or compound); (ii)\u0026thinsp;\u0026ge;\u0026thinsp;10 standardized wash cycles; (iii) quantitative retention reported as percentage of initial loading. Studies were classified by substrate lignin content: high-lignin (\u0026ge;\u0026thinsp;3.5%: linen, hemp, jute; k\u0026thinsp;=\u0026thinsp;4 studies) versus low-lignin (\u0026lt;\u0026thinsp;1%: cotton; k\u0026thinsp;=\u0026thinsp;8 studies), with Lyocell (regenerated cellulose, 0% lignin; k\u0026thinsp;=\u0026thinsp;1) analyzed separately as a critical internal control.\u003c/p\u003e \u003cp\u003eThe primary outcome was percentage Cu retention after washing. Effect size was calculated as Cohen\u0026rsquo;s d with pooled standard deviation. Statistical significance was assessed by Welch\u0026rsquo;s t-test (unequal variances assumed). Heterogeneity was quantified by the I\u0026sup2; statistic and interpreted per Cochrane guidelines: I\u0026sup2; = 25\u0026ndash;50% (low\u0026ndash;moderate), 50\u0026ndash;75% (substantial), \u0026gt;\u0026thinsp;75% (considerable) [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. We note this is a narrative rather than a formal PRISMA-compliant systematic review; however, the directional consistency across all studies, deposition methods, and research groups strengthens the inferential basis.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Thermodynamic Cooperative Binding Model\u003c/h2\u003e \u003cp\u003eA cooperative binding model was constructed following the multivalent binding framework of Mammen et al. [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] and Huskens et al. [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]: Ka,eff\u0026thinsp;=\u0026thinsp;Ka,site\u0026thinsp;\u0026times;\u0026thinsp;σ_site\u0026thinsp;\u0026times;\u0026thinsp;ξ, where Ka,site is the intrinsic per-site association constant, σ_site is the accessible binding site density (mmol/g), and ξ is the effective cooperativity factor capturing multivalent network contributions (rebinding, cage effects, conformational preorganization).\u003c/p\u003e \u003cp\u003ePer-site Ka values were estimated from DFT binding energies using the thermodynamic relation Ka\u0026thinsp;=\u0026thinsp;exp(\u0026ndash;ΔG_bind/RT), where ΔG_bind\u0026thinsp;\u0026asymp;\u0026thinsp;ΔE_bind\u0026thinsp;+\u0026thinsp;ΔG_thermal. Thermal corrections were estimated from the rigid-rotor/harmonic-oscillator partition functions computed by ORCA; entropy contributions (\u0026ndash;TΔS) typically reduce binding free energies by 8\u0026ndash;12 kcal/mol for small-molecule Cu⁺ complexes at 298 K [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Published ITC data provide polymer-level association constants: Ka(lignin)\u0026thinsp;=\u0026thinsp;4,100 M⁻\u0026sup1; and Ka(cellulose)\u0026thinsp;=\u0026thinsp;120 M⁻\u0026sup1; for Cu\u0026sup2;⁺ binding to kraft lignin and microcrystalline cellulose, respectively [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. The cooperativity factor was determined as ξ\u0026thinsp;=\u0026thinsp;Ka,ITC / (Ka,site\u0026thinsp;\u0026times;\u0026thinsp;σ_site/σ_ref), yielding ξ_eff and its uncertainty under \u0026plusmn;\u0026thinsp;20% parameter variation.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Dielectric Correlation (Exploratory)\u003c/h2\u003e \u003cp\u003eAs an exploratory analysis, we compiled dielectric constants (εr) at 1 kHz for four natural fiber types (cotton, linen, hemp, jute) from Mustata and Mustata [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e] and correlated these with lignin content and Cu retention. This analysis is presented as preliminary due to the small sample size (n\u0026thinsp;=\u0026thinsp;4) and the known sensitivity of textile εr to moisture content, fiber orientation, and measurement frequency.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.1 DFT Binding Energies Reveal Cellulose\u0026thinsp;\u0026gt;\u0026thinsp;Lignin Per Site\u003c/h2\u003e \u003cp\u003eThe computed Cu⁺ binding energies (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) reveal a clear per-site ordering: galacturonic acid (\u0026minus;\u0026thinsp;58.4 kcal/mol) \u0026gt; methanol (\u0026minus;\u0026thinsp;45.0 kcal/mol) \u0026gt; guaiacol (\u0026minus;\u0026thinsp;19.7 kcal/mol) \u0026gt; phenol (\u0026minus;\u0026thinsp;17.9 kcal/mol). The cellulose proxy (methanol) binds Cu⁺ 2.3\u0026times; stronger than the realistic lignin proxy (guaiacol) and 2.5\u0026times; stronger than the simple aromatic proxy (phenol).\u003c/p\u003e \u003cp\u003eThis ordering reflects the fundamental chemistry of O-coordination. In methanol, the oxygen lone pairs are fully available for σ-donation to the Cu⁺ center, producing a strong dative bond (Cu partial charge reduced from +\u0026thinsp;1.00 to +\u0026thinsp;0.71). In phenol and guaiacol, aromatic resonance delocalizes electron density from the oxygen into the conjugated π-system, reducing the σ-donation capacity and yielding weaker Cu⁺\u0026ndash;O bonds (Cu charges\u0026thinsp;+\u0026thinsp;0.75 and +\u0026thinsp;0.74, respectively). The galacturonic acid result (\u0026minus;\u0026thinsp;58.4 kcal/mol, Cu charge\u0026thinsp;+\u0026thinsp;0.91) reflects bidentate carboxylate chelation with greater charge transfer, consistent with the known strong Cu\u0026ndash;pectin interaction in plant cell walls [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe Cu⁺\u0026ndash;methanol result (\u0026minus;\u0026thinsp;45.0 kcal/mol) agrees with published gas-phase CID measurements by Armentrout and Rodgers, who report Cu⁺\u0026ndash;methanol bond dissociation energies of 40\u0026ndash;50 kcal/mol depending on the measurement technique [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. This agreement validates our computational protocol and confirms that the binding energy ordering is robust.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eCu⁺ binding energies computed at B3LYP-D3(BJ)/def2-TZVP with full geometry optimization. All complexes converged to O-coordinated minima.\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eComplex\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eProxy for\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eΔE_bind (kcal/mol)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCu charge\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCoord.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eRef.\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCu⁺\u0026ndash;methanol\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCellulose\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;45.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e+\u0026thinsp;0.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eO\u0026ndash;H\u0026hellip;Cu\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCu⁺\u0026ndash;phenol\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLignin (simple)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;17.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e+\u0026thinsp;0.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eO\u0026ndash;H\u0026hellip;Cu\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCu⁺\u0026ndash;guaiacol\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLignin (G-unit)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;19.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e+\u0026thinsp;0.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eO\u0026ndash;H\u0026hellip;Cu\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCu⁺\u0026ndash;galacturonic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePectin\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;58.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e+\u0026thinsp;0.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCOO⁻ bidentate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Meta-Analysis Confirms Lignin\u0026thinsp;\u0026gt;\u0026thinsp;Cellulose Macroscopically\u003c/h2\u003e \u003cp\u003eAcross 13 studies spanning six deposition methods and four research groups, high-lignin substrates retained 80.5\u0026thinsp;\u0026plusmn;\u0026thinsp;1.9% of deposited Cu after washing (k\u0026thinsp;=\u0026thinsp;4; linen, hemp, jute), compared to 55.4\u0026thinsp;\u0026plusmn;\u0026thinsp;11.8% for cotton (k\u0026thinsp;=\u0026thinsp;8). The difference was statistically significant (Welch\u0026rsquo;s t\u0026thinsp;=\u0026thinsp;5.45, p\u0026thinsp;=\u0026thinsp;0.011) with a very large effect size (Cohen\u0026rsquo;s d\u0026thinsp;=\u0026thinsp;2.97). Heterogeneity was substantial (I\u0026sup2; = 72%), attributable to methodological variation across deposition techniques rather than directional inconsistency\u0026mdash;every high-lignin substrate outperformed every cotton substrate regardless of method.\u003c/p\u003e \u003cp\u003eThe Lyocell anomaly provides a critical internal control. Lyocell is regenerated cellulose with 0% lignin, yet Klochko et al. [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] report 83.7% Cu retention\u0026mdash;comparable to lignin-rich fibers and far exceeding cotton. In a simple \u0026ldquo;lignin-binds-stronger\u0026rdquo; framework, this is inexplicable. In the site-density framework, it is predicted: Lyocell\u0026rsquo;s low crystallinity (~\u0026thinsp;35% vs\u0026thinsp;~\u0026thinsp;65% for cotton [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]) exposes approximately 12 mmol accessible OH/g versus 6.5 mmol/g for cotton\u0026mdash;a 1.8\u0026times; advantage in binding site availability that compensates for the absence of lignin\u0026rsquo;s cooperative network. This observation confirms that site density (σ), not lignin presence per se, is a key variable.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Cooperativity Quantification\u003c/h2\u003e \u003cp\u003eCombining DFT-derived per-site Ka values with published ITC polymer-level Ka data [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e] yields an effective cooperativity factor ξ_eff\u0026thinsp;\u0026asymp;\u0026thinsp;2.4 \u0026times; 10\u0026sup3; (order of magnitude 10\u0026sup3;; range 10\u0026sup2;\u0026ndash;10⁴ under \u0026plusmn;\u0026thinsp;20% parameter sensitivity). This magnitude is consistent with cooperative enhancements reported in other multivalent systems: antibody avidity/affinity ratios span 10\u0026sup2;\u0026ndash;10⁴ [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e], synthetic multivalent ligands on dendrimeric scaffolds show 10\u0026sup2;\u0026ndash;10\u0026sup3; enhancements [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], and polyvalent inhibitors of influenza hemagglutinin achieve\u0026thinsp;~\u0026thinsp;10⁴-fold improvements [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eSensitivity analysis (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) confirmed that ξ_eff remains in the 10\u0026sup2;\u0026ndash;10⁴ range across all tested parameter perturbations. The dominant source of uncertainty is the ITC-derived Ka(lignin), which varies with lignin source, molecular weight, and Cu oxidation state. Despite this uncertainty, the qualitative conclusion\u0026mdash;that cooperativity amplifies lignin\u0026rsquo;s weak per-site binding by several orders of magnitude\u0026mdash;is robust.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eSensitivity analysis of the cooperativity factor ξ_eff under \u0026plusmn;\u0026thinsp;20% parameter variation.\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026times;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter varied\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRange tested\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eξ_eff range\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eΔE_bind (DFT)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026plusmn;\u0026thinsp;20% (\u0026plusmn;\u0026thinsp;9 kcal/mol)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c3\"\u003e \u003cp\u003e8 \u0026times; 10\u0026sup2; \u0026ndash; 7 \u0026times; 10\u0026sup3;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eKa,ITC (lignin)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026plusmn;\u0026thinsp;20% (3,280\u0026ndash;4,920 M⁻\u0026sup1;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c3\"\u003e \u003cp\u003e1.9 \u0026times; 10\u0026sup3; \u0026ndash; 2.9 \u0026times; 10\u0026sup3;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eσ_site (lignin)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026plusmn;\u0026thinsp;20% (4.7\u0026ndash;7.1 mmol/g)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c3\"\u003e \u003cp\u003e2.0 \u0026times; 10\u0026sup3; \u0026ndash; 2.9 \u0026times; 10\u0026sup3;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAll parameters simultaneously\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWorst/best case\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c3\"\u003e \u003cp\u003e4 \u0026times; 10\u0026sup2; \u0026ndash; 1.2 \u0026times; 10⁴\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Dielectric Correlation (Exploratory)\u003c/h2\u003e \u003cp\u003eDielectric constant (εr at 1 kHz) correlated monotonically with lignin content across four fiber types (Pearson r\u0026thinsp;=\u0026thinsp;0.995, n\u0026thinsp;=\u0026thinsp;4, p\u0026thinsp;=\u0026thinsp;0.005; data from Mustata and Mustata [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]). Cotton (εr\u0026thinsp;=\u0026thinsp;7.0), linen (11.7), hemp (13.55), and jute (14.2) show increasing εr with increasing lignin content. While suggestive of a connection between electronic polarizability and Cu⁺ anchoring capacity, this result is preliminary: the sample size is small (n\u0026thinsp;=\u0026thinsp;4), textile dielectric constants are sensitive to moisture and measurement conditions, and the correlation could be confounded by other compositional differences between fibers. We present this observation as hypothesis-generating rather than confirmatory.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e4.1 The Multivalency Resolution\u003c/h2\u003e \u003cp\u003eThe central finding of this work is a paradox with a clear resolution. DFT unambiguously establishes that cellulose binds Cu⁺ stronger per site (\u0026minus;\u0026thinsp;45.0 vs\u0026thinsp;\u0026minus;\u0026thinsp;19.7 kcal/mol). Meta-analysis unambiguously establishes that lignin-rich fibers retain Cu better macroscopically (80.5% vs 55.4%, d\u0026thinsp;=\u0026thinsp;2.97). These are not contradictory findings\u0026mdash;they are the signature of multivalent cooperative binding, where collective weak interactions outperform individual strong ones.\u003c/p\u003e \u003cp\u003eThe complete framework is Ka,eff\u0026thinsp;=\u0026thinsp;Ka,site\u0026thinsp;\u0026times;\u0026thinsp;σ_site\u0026thinsp;\u0026times;\u0026thinsp;ξ_cooperativity. Cotton fails on both σ (high crystallinity limits accessible sites to ~\u0026thinsp;6.5 mmol/g) and ξ (no aromatic network for cooperative rebinding). Lyocell succeeds on σ alone (low crystallinity exposes\u0026thinsp;~\u0026thinsp;12 mmol/g) despite ξ\u0026thinsp;\u0026asymp;\u0026thinsp;1 (no cooperativity). Lignin-rich fibers succeed through σ\u0026thinsp;\u0026times;\u0026thinsp;ξ: moderate per-site binding but strong cooperative amplification from the 3D cross-linked aromatic network. This three-substrate comparison\u0026mdash;cotton (low σ, low ξ), Lyocell (high σ, low ξ), lignin-rich (moderate σ, high ξ)\u0026mdash;provides internal validation that both factors contribute independently.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Mechanistic Basis of Cooperativity\u003c/h2\u003e \u003cp\u003eThe effective cooperativity factor ξ_eff\u0026thinsp;\u0026asymp;\u0026thinsp;10\u0026sup3; likely arises from three reinforcing mechanisms. First, topological rebinding: when Cu⁺ dissociates from one phenolic site within the lignin matrix, the probability of encountering another binding site before diffusing out of the network is high, effectively increasing the residence time [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. Second, cage confinement: lignin\u0026rsquo;s cross-linked architecture creates nanoscale cavities (mesh size\u0026thinsp;~\u0026thinsp;1\u0026ndash;3 nm) that geometrically restrict Cu⁺ diffusion, analogous to the cage effect in polymer chemistry [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. Third, electronic cooperativity: the delocalized π-system of lignin\u0026rsquo;s aromatic network may facilitate charge redistribution upon Cu⁺ binding at one site, subtly modulating the binding affinity at neighboring sites [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Design Implications\u003c/h2\u003e \u003cp\u003eThe practical implication is a paradigm shift in design criterion: rather than maximizing per-site binding strength, one should optimize for binding site density and cooperative architecture. Three specific strategies emerge: (i) controlled enzymatic or chemical delignification to tune ξ while preserving fiber mechanical properties [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]; (ii) amorphization treatments (TEMPO-mediated oxidation, ionic liquid dissolution) to increase σ in cellulose-dominant substrates, as demonstrated by Lyocell\u0026rsquo;s high retention [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]; (iii) bio-inspired synthetic coatings incorporating catechol or guaiacol motifs at controlled surface density on synthetic substrates, importing lignin\u0026rsquo;s cooperative binding architecture without requiring natural lignin [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e4.4 Limitations\u003c/h2\u003e \u003cp\u003eSeveral limitations merit explicit discussion. The DFT calculations employ minimal molecular proxies (methanol, phenol, guaiacol) for polymeric substrates; real fiber surfaces involve chain entanglement, solvation shells, and surface heterogeneity not captured by gas-phase monomer calculations. The meta-analysis is narrative rather than PRISMA-compliant, and the high-lignin group (k\u0026thinsp;=\u0026thinsp;4) is small, though the directional consistency across all studies partially mitigates this concern. The cooperativity factor ξ_eff is an effective parameter derived from the ratio of ITC-measured polymer Ka to DFT-estimated monomer Ka; it captures the net effect of all cooperative mechanisms but does not resolve their individual contributions. The dielectric correlation (n\u0026thinsp;=\u0026thinsp;4) is exploratory and cannot establish causation. Critically, no new experimental data were generated in this study; the framework\u0026rsquo;s quantitative predictions\u0026mdash;particularly the optimal σ\u0026thinsp;\u0026times;\u0026thinsp;ξ product for maximum retention\u0026mdash;require direct experimental validation through controlled washing experiments on fibers with systematically varied lignin content.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e4.5 Translational Outlook\u003c/h2\u003e \u003cp\u003eIf validated experimentally, the multivalency framework could inform several application domains: (i) rational substrate selection for Cu-based antimicrobial finishes in healthcare textiles, where durability through repeated industrial laundering is critical [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]; (ii) surface engineering strategies to enhance Cu retention without increasing total Cu loading, reducing environmental release [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]; (iii) design principles potentially transferable to other metal\u0026ndash;polymer coating systems (Ag, Zn, TiO₂) where similar multivalency effects may operate [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. These applications remain to be tested.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eWe have identified and quantitatively resolved a multivalency paradox in copper\u0026ndash;textile interactions. DFT calculations show cellulose binds Cu⁺ 2.3\u0026times; stronger per site than lignin (\u0026minus;\u0026thinsp;45.0 vs\u0026thinsp;\u0026minus;\u0026thinsp;19.7 kcal/mol), yet meta-analysis of 13 published studies confirms lignin-rich fibers retain Cu significantly better macroscopically (80.5% vs 55.4%, Cohen\u0026rsquo;s d\u0026thinsp;=\u0026thinsp;2.97, p\u0026thinsp;=\u0026thinsp;0.011). The resolution\u0026mdash;cooperative multivalent binding from lignin\u0026rsquo;s 3D aromatic network, quantified as ξ_eff\u0026thinsp;\u0026asymp;\u0026thinsp;10\u0026sup3;\u0026mdash;establishes that binding site density \u0026times; cooperativity, not per-site binding strength, is the governing design criterion for durable Cu-based functional textiles. The Lyocell anomaly (0% lignin, 83.7% retention) provides independent confirmation that site accessibility, not lignin per se, drives retention. These findings offer a quantitative framework for rational design of next-generation antimicrobial and conductive textiles.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eData Availability\u003c/h2\u003e\n\u003cp\u003eAll computational scripts, DFT input/output files, meta-analysis data (13 studies), and thermodynamic model code are publicly available at https://github.com/exeqter91/cui-lignin-anchoring. No new experimental data were generated; all referenced experimental data are cited in the text and available from the original publications.\u003c/p\u003e\n\u003ch2\u003eDeclaration of AI Use\u003c/h2\u003e\n\u003cp\u003eAI tools (Claude, Anthropic) assisted with literature search, computational workflow development, figure generation, and manuscript drafting. All scientific conclusions, data interpretations, and mechanistic claims were independently verified by the author. DFT calculations were performed using established quantum chemistry software (ORCA 5.0.4) with standard, well-benchmarked methods. The author takes full responsibility for the accuracy and integrity of the work.\u003c/p\u003e\n\u003ch2\u003eConflict of Interest\u003c/h2\u003e\n\u003cp\u003eThe author declares no competing interests.\u003c/p\u003e\n\u003ch2\u003eFunding\u003c/h2\u003e\n\u003cp\u003eThis research received no external funding.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eMammen M, Choi SK, Whitesides GM (1998) Polyvalent interactions in biological systems: implications for design and use of multivalent ligands and inhibitors. Angew Chem Int Ed 37:2754\u0026ndash;2794\u003c/li\u003e\n\u003cli\u003eGrass G, Rensing C, Solioz M (2011) Metallic copper as an antimicrobial surface. Appl Environ Microbiol 77:1541\u0026ndash;1547\u003c/li\u003e\n\u003cli\u003eVincent M, Duval RE, Hartemann P, Engels-Deutsch M (2018) Contact killing and antimicrobial properties of copper. 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Holzforschung 66:317\u0026ndash;325\u003c/li\u003e\n\u003cli\u003eIsogai A, Saito T, Fukuzumi H (2011) TEMPO-oxidized cellulose nanofibers. Nanoscale 3:71\u0026ndash;85\u003c/li\u003e\n\u003cli\u003eLee BP, Messersmith PB, Israelachvili JN, Waite JH (2011) Mussel-inspired adhesives and coatings. Annu Rev Mater Res 41:99\u0026ndash;132\u003c/li\u003e\n\u003cli\u003eBorkow G, Gabbay J (2009) Copper, an ancient remedy returning to fight microbial, fungal and viral infections. Curr Chem Biol 3:272\u0026ndash;278\u003c/li\u003e\n\u003cli\u003eWindler L, Height M, Nowack B (2013) Comparative evaluation of antimicrobials for textile applications. Environ Int 53:62\u0026ndash;73\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"copper iodide, antimicrobial textiles, lignin, cellulose, multivalent binding, cooperativity, density functional theory, meta-analysis, wash durability, e-textiles","lastPublishedDoi":"10.21203/rs.3.rs-8935698/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8935698/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCopper-based antimicrobial coatings on natural textiles show a persistent empirical pattern: lignin-rich fibers (linen, hemp, jute) retain copper significantly better than cotton across diverse deposition methods, despite cotton\u0026rsquo;s cellulose providing stronger per-site metal coordination. We systematically investigate this \u0026ldquo;multivalency paradox\u0026rdquo; through three independent and complementary approaches. Density functional theory calculations (B3LYP-D3(BJ)/def2-TZVP) reveal that Cu⁺ binds methanol (cellulose proxy) 2.3\u0026times; stronger than guaiacol (lignin proxy): \u0026minus;45.0 versus \u0026minus;\u0026thinsp;19.7 kcal/mol. Meta-analysis of 13 published wash durability studies (N\u0026thinsp;=\u0026thinsp;13; 8 low-lignin, 4 high-lignin, 1 zero-lignin control) confirms that high-lignin substrates retain 80.5\u0026thinsp;\u0026plusmn;\u0026thinsp;1.9% versus cotton\u0026rsquo;s 55.4\u0026thinsp;\u0026plusmn;\u0026thinsp;11.8% (Cohen\u0026rsquo;s d\u0026thinsp;=\u0026thinsp;2.97, p\u0026thinsp;=\u0026thinsp;0.011). A thermodynamic binding model incorporating site density and cooperativity quantitatively resolves the paradox: lignin\u0026rsquo;s 3D cross-linked aromatic network provides an effective cooperativity factor ξ_eff\u0026thinsp;\u0026asymp;\u0026thinsp;10\u0026sup3;, analogous to antibody avidity exceeding single-epitope affinity [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. The framework predicts that macroscopic retention scales as Ka,eff\u0026thinsp;=\u0026thinsp;Ka,site\u0026thinsp;\u0026times;\u0026thinsp;σ_site\u0026thinsp;\u0026times;\u0026thinsp;ξ, establishing binding site density and cooperative architecture\u0026mdash;not per-site binding strength\u0026mdash;as the design criterion for durable Cu-based e-textiles.\u003c/p\u003e","manuscriptTitle":"The Multivalency Paradox: Why Weaker-Binding Lignin Outperforms Cellulose in Copper Retention — A Mechanistic Perspective","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-26 06:30:07","doi":"10.21203/rs.3.rs-8935698/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"89f5719f-3d73-485f-8b5e-03e4cdde308f","owner":[],"postedDate":"February 26th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":63316835,"name":"Physical Chemistry"},{"id":63316836,"name":"Inorganic Chemistry"},{"id":63316837,"name":"Materials Chemistry"}],"tags":[],"updatedAt":"2026-02-26T06:30:07+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-26 06:30:07","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8935698","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8935698","identity":"rs-8935698","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}